The Advtrains mod for Luanti

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4 Interlocking design

Unlike the previous section, this section primarily focuses on the theoretical aspect where certain details of interlocking become irrelevant.

4.1 Conflict-free routes in junctions

Track sections in junctions should generally be deignated in a way that guarantees train safety while also allowing high throughput.

Consider the following example:

(-tikz- diagram)

In the diagram above, the TCBs at P and Q are not strictly necessary for safety. However, omitting the two TCBs would cause the entire junction to be set up as a single track section, which would prevent two trains from using the junction even if they would not collide. An example of two non-conflicting routes is marked in the diagram.

A general method to add TCBs is to identify non-conflicting routes and add TCBs to tracks that cross such routes. This theoretically involves inspecting \(O(n^2)\) pairs of routes, but the number of pairs tends to be low for relatively simply junctions and can be further reduced using certain properties.

Consider the possible routes:

  • • A1→B1

  • • A1→C1

  • • B2→A2

  • • C2→A2

Checking all possible pairs of routes for conflicts would involve checking 6 pairs:

  • • A1→B1 and A1→C1

  • • A1→B1 and B2→A2

  • • A1→B1 and C2→A2

  • • A1→C1 and B2→A2

  • • A1→C1 and C2→A2

  • • B2→A2 and C2→A2

It is not hard to see that two routes inevitably collide if they share the same origin (A1→B1 and A1→C1) or the same destination (B2→A2 and C2→A2). We therefore do not need to inspect these pairs further.

Next, consider that the exact geometry of the tracks is not important for checking conflicts if the relation of the tracks (i.e. whether two tracks cross each other) and track components (i.e. whether a TCB splits the track into two sections) is preserved. In this context, the two track layouts are functionally equivalent, and they are both symmetric:

(-tikz- diagram)

It is possible to observe that B1 and C2 are symmetric. Similarly, the routes A1→B1 and C2→A2 are symmetric if directionality is ignored.7

Consider the routes A1→B1 and B2→A2. It is clear that two trains traveling on the two routes cannot collide with each other. It is therefore sensible to split the junction into at least two sections such that the two routes do not occupy the same section. In this example, this can be done by placing a TCB at P.

The symmetry of the junction can be used to conclude that the routes C2→A2 and A1→C1 do not have collisions either. This can be allowed by adding a TCB at Q, which is also symmetric to the TCB at P:

(-tikz- diagram)

Note that the axis of symmetry also splits the junction. The routes A1→B1 and C2→A2 do not conflict with each other as both routes are on different sides of the axis of symmetry and neither route crosses the axis. However, the TCBs at P and Q already split the junction in a way that the two routes do not share the same section, so no further TCBs need to be added.

Finally, observe that A1→C1 and C2→A2 always conflict with each other, so it is not possible to split the junction in a way that prevents the two routes from conflicting.

7 The collision of two routes is ultimately determined by the presence of conflicts (in particular, intersections) between the paths of two routes. The direction in which the routes are traversed do not affect the presence of conflicts.

4.2 Track capacity and deadlock

It is not possible to run an infinite number of trains on a line. Adding too many trains to a line can result in a deadlock, where every train is stuck at a red signal, waiting for the previous train to clear the track section ahead, while the previous train is also stuck at a red signal, waiting for the train ahead of it to leave the section ahead, and so on:

(-tikz- diagram)

This problem can be trivially solved by removing a train and, if necessary, resetting the track section that the train previously occupied (this can be done in the track section formspec):

(-tikz- diagram)

However, only the train at the bottom-right can move; other trains have to wait for the trains ahead to leave the section. The ideal situation is that the section length and the number of trains are decided in such a way that trains do not have to stop or slow down between stations:

(-tikz- diagram)

When actually building a rail line, signals are spaced away much further than in the illustration above. On servers, the distance between signals typically range between about 50 nodes to a few hundred, depending on the speed at which trains run on the line and the number of trains using the line. The distance between signals in station areas usually depend on the size of the station.

Single-track sections can also be a source of deadlocks:

(-tikz- diagram)

With single-track sections, routes should generally be set up in a way that the train does not stop in single track sections (like train A in the above diagram):

(-tikz- diagram)

In the modified setup, the leftmost signal requires the entire marked area to be clear, avoiding the deadlock situation described earlier. However, this also reduces the capacity of the line.

Note that the end of the track (e.g. train B) is an exception, where the train has to stop and reverse. Removing train B in the original setup is not guaranteed to resolve the deadlock, as a train approaching from the west may enter the area, restoring the original situation.

Another way of observing train B is to replace the dead end with a balloon loop:

(-tikz- diagram)

Single-track sections and scheduling

The capacity of lines with single-track sections can be analyzed using graphic timetables:

(-tikz- diagram)

In this example, trains A and C can occupy different tracks of the passing loop at the same time, while the schedules for trains B and C conflict with each other as the two trains would occupy the same track at the same time.

4.3 Short routes

In some cases, there may be setups with very short routes. In particular, if the length of a route is shorter than the braking distance of the train for which the route is set, the signal at the end of the route will be triggered to set a route.

If short routes are desired, such as at stations, it is generally recommended to disable ARS for the train, such as by using the A0 ATC command, and keep some distance between the influence point of the signal and the point at which the train is expected to stop. Alternatively, you can also limit the speed of the train to trigger the routesetting system later, but this is not the ideal solution in most use cases of short routes.